Question: Let $g(x)=x^{-12}$. $g'(x)=$
Explanation: The derivative of $g$ can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a negative number.) $\begin{aligned} &\phantom{=}g'(x) \\\\ &=\dfrac{d}{dx}\left(x^{-12}\right) \\\\ &=-12x^{-12-1} \gray{\text{The power rule}} \\\\ &=-12x^{-13} \end{aligned}$ In conclusion, we found that $g'(x)=-12x^{-13}$. This can also be written as $-\dfrac{12}{x^{13}}$ (all equivalent forms are accepted).